Related papers: Non-exchangeable random partition models for micro…
Traditional Bayesian random partition models assume that the size of each cluster grows linearly with the number of data points. While this is appealing for some applications, this assumption is not appropriate for other tasks such as…
Bayesian nonparametric approaches, in particular the Pitman-Yor process and the associated two-parameter Chinese Restaurant process, have been successfully used in applications where the data exhibit a power-law behavior. Examples include…
Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…
We study random families of subsets of $\mathbb{N}$ that are similar to exchangeable random partitions, but do not require constituent sets to be disjoint: Each element of ${\mathbb{N}}$ may be contained in multiple subsets. One class of…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…
Recent advances in Bayesian models for random partitions have led to the formulation and exploration of Exchangeable Sequences of Clusters (ESC) models. Under ESC models, it is the cluster sizes that are exchangeable, rather than the…
For any partition of $\{1, 2, ..., n\}$ we define its {\it increments} $X_i, 1 \le i \le n$ by $X_i = 1$ if $i$ is the smallest element in the partition block that contains it, $X_i = 0$ otherwise. We prove that for partially exchangeable…
Kingman derived the Ewens sampling formula for random partitions from the genealogy model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process. M\"ohle described the recursion which…
By resorting to sequential constructions of exchangeable random partitions (Pitman, 2006), and exploiting some known facts about generalized Stirling numbers, we derive a generalized Chinese restaurant process construction of exchangeable…
Although exchangeable processes from Bayesian nonparametrics have been used as a generating mechanism for random partition models, we deviate from this paradigm to explicitly incorporate clustering information in the formulation of our…
We introduce a general Bayesian framework for graph matching grounded in a new theory of exchangeable random permutations. Leveraging the cycle representation of permutations and the literature on exchangeable random partitions, we define,…
Suppose some random resource (energy, mass or space) $\chi \geq 0$ is to be shared at random between (possibly infinitely many) species (atoms or fragments). Assume ${\Bbb E}\chi =\theta <\infty $ and suppose the amount of the individual…
Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process…
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing…
Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process, and…
We develop the distance dependent Chinese restaurant process (CRP), a flexible class of distributions over partitions that allows for non-exchangeability. This class can be used to model many kinds of dependencies between data in infinite…
We consider a family of distributions on spatial random partitions that provide a coupling between different models of interest: the ideal Bose gas; the zero-range process; particle clustering; and spatial permutations. These distributions…
Feature allocation models are popular models used in different applications such as unsupervised learning or network modeling. In particular, the Indian buffet process is a flexible and simple one-parameter feature allocation model where…
We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…
We use a natural ordered extension of the Chinese Restaurant Process to grow a two-parameter family of binary self-similar continuum fragmentation trees. We provide an explicit embedding of Ford's sequence of alpha model trees in the…